Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

Entropy

Mariana Krasnytska¹  Yurij Holovatch¹  Ralph Kenna²  Bertrand Berche² 

[1] Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine;\({{\mathbb L}^4}\) Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry;

关键词: Ising model;    scale-free network;    self-averaging;    steepest descent;   

DOI  :  10.3390/e23091175

来源: DOAJ

【 摘 要 】

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.

【 授权许可】

Unknown